# M2 ProjectilesWatch

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Thread starter 7 years ago
#1
I'm given the equation .
From this I'm meant to show that the maximum value of as varies is and that this is achieved when .

I get that the maximum value of occurse when , giving me the quadratic equation . Solving this quadratic gives me , which kinda looks like what I'm aiming for, but it isn't quite right. Can anyone tell me what I should be doing?

Thanks for any help.

ETA: This isn't the full question - the first part is where the projectiles element is, and all it asks is to derive the first equation given above (which wasn't a problem).
0
7 years ago
#2
For the first bit, there may be better ways, but you can differentiate the expression w.r.t theta. Then as dx/dtheta = 0 at max, 3 of the terms go away, leaving a nice tan theta = a/x.

Now sub this tan theta back into the original expression to get what you need.

Then for the next bit, sub this value of x back into the tan theta = a/x bit (found earlier) and you're there.

Bric
0
7 years ago
#3
(Original post by Bric)
For the first bit, there may be better ways, but you can differentiate the expression w.r.t theta. Then as dx/dtheta = 0 at max, 3 of the terms go away, leaving a nice tan theta = a/x.

Now sub this tan theta back into the original expression to get what you need.

Then for the next bit, sub this value of x back into the tan theta = a/x bit (found earlier) and you're there.

Bric
You can get the tan = a/x by completing the square
0
Thread starter 7 years ago
#4
(Original post by Bric)
For the first bit, there may be better ways, but you can differentiate the expression w.r.t theta. Then as dx/dtheta = 0 at max, 3 of the terms go away, leaving a nice tan theta = a/x.

Now sub this tan theta back into the original expression to get what you need.

Then for the next bit, sub this value of x back into the tan theta = a/x bit (found earlier) and you're there.

Bric
Thanks, seems I'll have to complete C3 and C4 before tackling questions like this.
0
7 years ago
#5
(Original post by Julii92)
Thanks, seems I'll have to complete C3 and C4 before tackling questions like this.
On the spec, it says prior knowledge is C1/C2/C3/M1
I tried M2 but gave up after I saw trig identities.
0
Thread starter 7 years ago
#6
(Original post by Jammy4410)
On the spec, it says prior knowledge is C1/C2/C3/M1
I tried M2 but gave up after I saw trig identities.
I think it says C4 aswell - for OCR in any case.
0
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